Problem: On the way to school, Karen became fixated on the puzzle game on her phone!

<image>

The game is played as follows. In each level, you have a grid with n rows and m columns. Each cell originally contains the number 0.

One move consists of choosing one row or column, and adding 1 to all of the cells in that row or column.

To win the level, after all the moves, the number in the cell at the i-th row and j-th column should be equal to gi, j.

Karen is stuck on one level, and wants to know a way to beat this level using the minimum number of moves. Please, help her with this task!

Input

The first line of input contains two integers, n and m (1 ≤ n, m ≤ 100), the number of rows and the number of columns in the grid, respectively.

The next n lines each contain m integers. In particular, the j-th integer in the i-th of these rows contains gi, j (0 ≤ gi, j ≤ 500).

Output

If there is an error and it is actually not possible to beat the level, output a single integer -1.

Otherwise, on the first line, output a single integer k, the minimum number of moves necessary to beat the level.

The next k lines should each contain one of the following, describing the moves in the order they must be done:

  * row x, (1 ≤ x ≤ n) describing a move of the form "choose the x-th row". 
  * col x, (1 ≤ x ≤ m) describing a move of the form "choose the x-th column". 



If there are multiple optimal solutions, output any one of them.

Examples

Input

3 5
2 2 2 3 2
0 0 0 1 0
1 1 1 2 1


Output

4
row 1
row 1
col 4
row 3


Input

3 3
0 0 0
0 1 0
0 0 0


Output

-1


Input

3 3
1 1 1
1 1 1
1 1 1


Output

3
row 1
row 2
row 3

Note

In the first test case, Karen has a grid with 3 rows and 5 columns. She can perform the following 4 moves to beat the level:

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In the second test case, Karen has a grid with 3 rows and 3 columns. It is clear that it is impossible to beat the level; performing any move will create three 1s on the grid, but it is required to only have one 1 in the center.

In the third test case, Karen has a grid with 3 rows and 3 columns. She can perform the following 3 moves to beat the level:

<image>

Note that this is not the only solution; another solution, among others, is col 1, col 2, col 3.

Solution (in PYTHON3):

Solution:
(n,m) = (int(i) for i in input().split())
tbl = []
for i in range(n):
	crstr = [int(j) for j in input().split()]
	tbl.append(crstr)
true=0


def prt():
	for xx in range(n):
		for yy in range(m):
			print(tbl[xx][yy], end='	')
		print()
	print()
	print()

# prt()
def lines():
	rows = []
	for i in range(n):
		while 1:
			may = 1
			for j in range(m):
				if tbl[i][j]==0:
					for k in range(j):
						tbl[i][k]+=1
					may = 0
					break
				tbl[i][j]-=1
			if not may: break
			rows.append(i+1)
		# prt()
	return rows

def cols():
	stolbs = []
	for i in range(m):
		while 1:
			may = 1
			for j in range(n):
				if tbl[j][i]==0:
					for k in range(j):
						tbl[k][i]+=1
					may = 0
					break
				tbl[j][i]-=1
			if not may: break
			stolbs.append(i+1)
		# prt()
	return stolbs

if m>n:
	l = lines()
	c = cols()
else:
	c = cols()
	l = lines()

br = 0
for i in range(n):
	for j in range(m):
		if tbl[i][j]!=0:
			br = 1
			break
	if br: break
if br:
	print(-1)
else:
	print(len(l)+len(c))
	for i in l:
		print('row', i)
	for i in c:
		print('col', i)